#!/usr/local/bin/python
# latlontools.py
# python script for Session 4,GEO 825
# Written by A. Shortridge, 1/2005, 1/2007, 1/2009

def dms2dd(dms = (42, 44, 9)):
    '''Converts a tuple of lat or lon in DMS to decimal degrees.
    
    Function returns a floating point number in dd.'''
    positive = 1
    if dms[0] < 0:
        positive = -1
    Deg = abs(dms[0])
    Min = dms[1]
    Sec = dms[2]
    dd = positive * (int(Deg) + ((float(Min) + (float(Sec)/60.0))/60))  # casting the min and sec is probably not needed
    return(dd)

def dd2dms(dd = 42.7358):
    '''Converts a decimal degree value to a tuple of DMS.
    
    A DMS tuple looks like this:  (Deg, Min, Sec).'''
    
    Deg = int(dd)
    ms = (abs(dd)%1) * 60  # Take the fractional part. Be sure it is positive!
    Min = int(ms)
    Sec = (ms%1) * 60
    dms = (Deg, Min, Sec)
    return(dms)

def haversine(p1, p2):
     '''Returns the distance between two points stored in lat lon (decimal deg).
     
     The points must be tuples, where p[0] is the lat and p[1] is 
     the lon. The function uses the Haversine formula to return a value, 
     in kilometers. See the URL:
     http://www.movable-type.co.uk/scripts/gis-faq-5.1.html'''
     
     import math
     earth_radius = 6371.009  # http://en.wikipedia.org/wiki/Earth_radius
     rc = 0.017453293  # degree to radian conversion (rc): pi / 180
     pt1 = (p1[0] * rc, p1[1] * rc) # change elements in p1 to radians, not degrees
     pt2 = (p2[0] * rc, p2[1] * rc) # change elements in p2 to radians, not degrees
     
     # Next, calculate the differences between the two lons and the two lats.
     dlon = pt2[1] - pt1[1]
     dlat = pt2[0] - pt1[0]
     
     # Finally, the math. See the URL above to learn what a, c, and d are.
     a = math.sin(dlat/2.0)**2 + math.cos(pt1[0]) * math.cos(pt2[0]) * math.sin(dlon/2.0)**2
     c = 2 * math.asin(math.sqrt(a))
     d = earth_radius * c
     return(d)


# The rest is a little test, with some data
EL = ((42,44,9), (84,29,4))
Det = ((42,22,59), (83,6,8))
Kal = ((42,16,29), (85,35,18))
AA = ((42,16,31), (83,43,51))
Lan = ((42,42,33), (84,33,14))
GR = ((42,57,41), (85,39,21))
SSM = ((46,29,4), (84,21,56))

# pts generated by OpenError lib to test for accuracy
# NOTE - pts gathered while random lat was used for cos function
pts =[(0.17822394128032967,0.49288321575025096),(1.4960280528300296,-0.04364273337995361),(-1.0205966628497027,-0.3445652986480711),(0.22950432589463718,0.471183885774541),(-1.4647876927799908,-0.711158824413519),(0.957410076124123,0.3828021293843127),(-0.5791680709653569,0.30883815193750097),(1.5273916477696048,-1.0506249580334195),(-1.2125081758447518,-0.6136538765737998),(0.13564793389674545,0.13915829862488585),(0.13466665006554387,-0.3405981654421369),(0.5534550414191256,-0.8737908259648092),(1.4019301165540414,0.4230320635007271),(1.941923794677482,-0.6801607178576888),(-0.17203915288280344,-0.3645847543040846),(1.2456935416128705,0.13742314107402667),(-0.5198167051069708,0.22550014807759652),(-0.6678432201942898,0.9532569887195049),(0.18061066463547965,1.1684169681372496),(-1.8013114655900526,-0.2525853774446591),(-0.49564232130277897,-1.1120503274237272),(-0.1497277094308372,1.0224062052904581),(-0.9722171218465394,-0.7023847766955402),(-0.7378259346527557,-0.811760334521466),(-0.26923057441997944,0.5992737730741357),(0.35169165538978014,0.671909206133468),(0.8167238189526328,-0.7681317406519563),(1.5802967034591917,0.9917223740695786),(0.45157527476583587,1.0935999015190891),(0.2676573452334358,0.02560008030298959),(-0.5786194055390543,0.0183768123461406),(0.09906627190702635,-0.5870609619299144),(-0.46387025782279406,0.783035616397675),(-0.1459597454530031,-0.5682653961702788),(-0.8345194561588798,1.0157391143963963),(0.5588823847149621,-1.6243932452441292),(-0.8031410617643294,-0.9367704866122839),(-0.440508149249899,-0.715778007044677),(-0.73328223257005,-1.5449319303210358),(0.028058745074930894,0.656787163647059),(0.6053451168020192,-1.2352525370506646),(-0.5653906349300376,0.9028466853806223),(-0.4107202105159728,-0.4536413285078307),(1.448447532952731,0.698422305894869),(-0.19571557354588406,-0.43441550997093814),(0.877130400933286,0.020440682442475485),(-1.545721208155912,1.3943221219176134),(1.8074285922893338,0.5113367518404797),(-0.3227697287314828,-0.13683915158162538),(0.9584073159006464,0.04111540093773148),(1.0524197363586618,1.1610437163582712),(-1.0597534558297448,-0.4100652333390261),(-0.3969730578990658,0.07244210176620033),(-0.20547667193605407,1.0392835752416743),(0.29446030290746167,0.5608871467794545),(0.07278220484880366,-1.14823164686362),(-1.2124584347511564,1.3364475989012288),(0.1642979505869809,-0.07339739971919744),(0.933013219688718,1.1112667611871905),(-0.093276905989454,0.0642291526640095),(-0.3876906007386753,0.010602010889551615),(0.939378682936241,0.49932072716926795),(0.4959303002305209,-0.2591608568616542),(-0.05737911948832068,1.0234598978954768),(0.8842639163968886,-2.069234062733001),(-0.42904717046802887,1.1207651502455998),(1.6704745838377806,-0.4124938230349297),(1.0294065807585717,0.3894202940102261),(0.19541584167837892,-0.21312254695247534),(-1.6715940107372718,0.5676441051610983),(0.4478501911787254,-0.728294118739157),(-0.03188789664144774,0.23234026226396434),(-0.3624312291112932,-0.8258595090284644),(-0.6660725282289883,0.09358454222090928),(-1.3654855616502017,0.6792609473515882),(0.1742341173274651,1.264546111479473),(-0.4217612963133052,-0.05641887439650671),(0.3235156096431589,-1.52244516010191),(0.7123267032598145,0.09659103005996576),(-0.37843772811172116,0.6296379849638122),(-1.624570428566419,-0.586433678840523),(1.4165367812800638,1.2780703658773467),(0.6855129424526339,1.0869670658060178),(-1.2880844674386978,0.4663051066854835),(1.944100300304368,-3.3551131169867205),(1.0792859278038158,-0.6080486239030852),(0.3998302757629868,0.30822430909340137),(-0.3731172162650119,-0.27663027983690597),(0.747612347934175,0.4139787819561103),(0.6280823397717138,-0.5132685445393288),(0.46256192889857645,0.9263008509878695),(-0.26022581972493203,-2.0782769475508256),(0.5270355389552546,1.167917169100963),(2.6096296094845393,-0.4385673380905276),(-0.6163040013360375,0.3601840589416387),(1.2802001522159125,-0.019868903498362997),(-0.3629600497220429,0.14035161871864354),(1.3869537234791423,1.1032692149566858),(-0.10691685607405225,1.5717875903329697),(0.8289907045751016,-0.6891252927849417)]
pts2 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# NOTE - pts gathered after data lat is used for cos function
pts3 = [(0.6433051730581724, 1.8389617392408397), (-1.0725858150871133, -0.20922662602824174), (-0.43822831123986017, -1.6066043889813542), (-0.8102013377047469, -2.03335811027234), (0.43632732150094533, -0.6907563288481471), (0.5461629524928472, -0.5149097384999932), (0.405857438304739, 0.095522553686938), (-0.3431527018580533, -0.6255809396229388), (-0.4623639776012795, -0.7614408650599488), (0.6078061872850401, -1.0284713822474976), (0.00011138144147059139, -2.422185292359227), (-0.03677676865684104, 0.2957601722560419), (-0.5856801787300178, 0.18169538995076318), (-1.230494657809528, 0.5444056199835109), (-0.6480436135880684, 0.19136584007010066), (-0.9627773867653401, 0.1920369114568825), (0.4220923188815914, -0.7060637353516236), (-0.5042955424528026, 0.2468799806803388), (-1.9146967906564605, 0.6526217077328367), (0.740828048056332, 0.6234867456156016), (-0.06664008022726092, -0.16482047453389226), (0.6174115618593987, -0.7893030153904376), (-0.47249067793536415, -0.9037684366063592), (0.0892504105167656, 0.9445747496287288), (1.260808016277132, 2.602147639052656), (0.5537536343115564, 0.22121310903058006), (-0.21537714904500752, 0.10273429296168411), (0.07247412572476604, 0.7232982395897251), (-0.020935157412744543, -0.2917749345715744), (0.48229095310571946, -0.019367112038195168), (0.03522069476062909, 0.963453876592981), (0.7874026459671681, -1.3882258545216801), (-0.2913941628343366, -0.025530260963678015), (1.6897779955099743, -1.0842908523788974), (-1.7216636074018024, -0.9541906025973109), (0.5795288859222631, 0.33639375875797994), (0.45910321965599205, 0.14279518032994942), (0.27444294850881096, -0.9901731660680587), (-0.25966694232582976, 1.849200364796656), (0.7143507745598185, -0.6717250464592333), (-0.06763257211744285, 0.9750308418185406), (0.5744102050558723, 0.5708607419591666), (0.36714468760185476, -0.4433036761437681), (-0.4946789525432122, -1.0323048270416297), (1.1095106196057427, -0.02728317143201309), (0.703184477554171, -1.5087413967303336), (0.11823946426160022, 1.1699031190876787), (-0.905001311876478, 0.3906498895765217), (-0.313656166603524, -0.5821861181941005), (-0.4233233237317, 0.13441801827586075), (0.05182634555956126, 0.9350367002588507), (1.0195061882949772, -0.3345232754370083), (0.6602075856666629, -1.3393790181700356), (0.9486909981779235, 0.6665424766702942), (1.0802705749971002, 2.0370137527587646), (0.2822496607318648, 0.2424893481018961), (-0.48430748608147606, -0.24055308770409034), (-1.098345913314913, 0.6756354225184891), (-0.21532729378255563, 0.9787742213748214), (0.2233468882434375, -2.167992551734471), (-0.5253843074691606, 1.285597189626525), (0.12815391910325555, -1.2167482057572705), (0.06993915275958466, -0.5338303112548332), (0.7342695794416559, 1.0039190087289427), (0.6209515593292436, 0.5763333623606056), (-1.1783173790591288, -0.4775769117623576), (0.9930535521317343, -1.592968275962978), (0.3232698262488778, 0.5212544144079643), (-0.25007532538612426, -1.622879604102449), (0.2509446487497825, 0.08730324303590194), (0.4741550482277956, -1.3044299335541119), (0.6490836146485137, -0.4344590705366984), (1.3370942458360473, 0.2964072644029341), (-0.536498211111943, 1.6828495256179654), (-1.3873767118384612, 1.4625579328320912), (0.012382320318958227, 0.24458458179375325), (-1.1149625931573024, 0.017296097403322375), (1.4564052948886612, 0.5608299105641292), (-1.0435126023989911, 0.14361555295667824), (-0.19167447960821996, 0.4425346536675976), (0.5110242453757512, -0.5076518214915118), (0.05046424691685346, -0.9704675587739701), (-0.8280332412904654, 0.4260075837399506), (-0.5975644462559407, 2.2332468410570305), (0.6638340735398661, 1.2870883433433387), (0.6024101435128092, -0.696711348925608), (1.0075485395672232, 1.0245121533357056), (0.1325348059099784, -1.2887587275232808), (0.2837897007636149, -1.2993115662693941), (-0.015701614525884245, 0.7328044136810825), (-0.22222350027735244, -0.8142485675679737), (-1.171616116546015, -0.5343191601850626), (0.7365409491321189, 0.6461618041360863), (-2.583831993179829, 0.8338730008549021), (0.634361529009937, -1.5297899347615078), (1.231390328908318, -0.522461762509383), (-0.010621887075361384, 0.4764885979513572), (0.03264155187520406, -0.10442392999551643), (-0.31962950729258693, 0.811738548641387), (-0.3138880981564622, 1.269791199524125), (-1.2686145649835123, 0.48775517533830004), (0.4432007028399421, -0.17619740060763658), (-0.23506157755494622, 0.8349063583773607), (0.43577329972971485, 0.1624665691049331), (-1.0125845917512395, 0.8099737893889618), (0.1268906059315812, 0.3127659508418633), (-1.563383209805943, -0.4701406468943351), (-0.25981625400405395, 0.6825897561509099), (-0.013273292570646977, -0.9507060307694877), (-1.255779358341497, -1.6222763725991882), (0.4564537360294985, -0.4996029077038112), (0.8471694373504125, 0.8773857914953086), (0.013661474436595105, 0.039701804108054996), (0.5225290989442826, 0.7452204875332257), (1.4151166616059396, -0.6152079594407893), (1.4817557077805108, -0.11170782468216466), (1.3511266734318221, 0.49030988740801423), (-0.6008845821581836, 0.22598896096147802), (-0.8242788957832594, -0.6059339461579655), (-0.43050485093714613, -0.19753332584635153), (-0.5311320481463555, 1.0564268589812222), (0.5223693989980728, 0.2310434815789048), (0.43533729506366947, -1.4827895732285326), (0.05064401209052777, -0.9039531578462215), (-0.22084401952899468, -0.04192714124875922), (1.450399485536173, -0.3860557505872331), (-0.9026400681505223, 0.41248862021309696), (0.5196824358158347, -1.264526318123326), (0.4897993124361145, -0.5283682936784155), (-0.04939335523265739, -0.5621877725174866), (0.818617290424843, -0.07143814359257265), (0.6193298818933014, -0.6543781322627762), (-1.1236745041768517, 0.38622205216575195), (1.0275929869224627, 0.4973389268808681), (-1.0697918509114288, -1.607849193141376), (-1.0290452987428478, 1.5968325422847658), (-0.21498095245676913, -0.28987030164125416), (-0.006790090033176689, -0.5590970010502373), (-0.04437563413763823, 0.5919301820100342), (0.41149444534289903, -0.6757191439820806), (0.2883379386433987, -0.16774615992431027), (0.07647317298010393, 0.7482967582329553), (-0.09570156987934454, 0.3583474840457164), (-0.5074034232912575, -0.8494143898076151), (-1.5985473336641762, 0.13945337591400503), (0.08581058264012971, -0.07741318139137743), (0.09166748156394457, -0.9422723101173086), (0.6672317864892257, 0.3188151787793906), (0.4212299218440047, -0.5622145981001798), (1.5035421096810304, 1.1658510138774334), (0.6918711739368327, -1.5930207857661607), (-0.15153705290208758, -1.5723054937140009), (0.9705013962914295, 0.015104687957786122), (1.0962649156963304, 0.783584890677899), (0.37581233145642323, 0.4905302587337553), (0.6566517431201155, 2.577662835025756), (-0.07729062802505193, -0.2916303995486794), (2.627078726264556, 0.10784843402220526), (0.4705733440144117, -1.87245202547539), (-0.3187531549533069, 0.8132889425174582), (-1.2712857288828774, 0.8263932190244988), (-0.22484767059459848, -0.11786167568161185), (0.40752882077098646, -1.0875232809925184), (-0.4231479181125248, -0.48788622679457294), (-0.8131352507539289, 0.21777604857673252), (-0.5537277866233057, -1.3874891934375866), (1.1905707746006915, -1.4778179044543678), (0.0038470198181333147, -0.8351892134498234), (0.30155914684329704, -0.881308731077048), (-0.6716792817543199, 1.0794388233775938), (0.25782499488441024, -1.2078672766861291), (-0.3794654912638896, -0.8400802163322965), (-0.4634972861949373, 0.8286002895568135), (0.9847985413907366, -0.5391955428673679), (-1.0386681867687588, -1.0716922545949303), (0.17427127252155974, -1.5067338835912245), (-0.806041882458337, 0.13425910518019912), (0.1898923315035787, -0.09629323406164275), (-0.03827366197778241, -1.8098330130055928), (1.0123363931193021, 0.22951004232700006), (0.15311305417589763, -0.4215326672634965), (-1.44188801411234, 1.3273481815832953), (1.4285435686091195, 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-1.2159499084495387), (0.41557720179762747, -1.2856901585656282), (0.7696599885420035, -0.6439356978153428), (0.21432552849889297, 1.0604245230205156), (-0.5555440114599748, 0.13384196373959245), (0.5350629797061229, 1.3916694192645656), (-1.2820067882295625, -0.6606673782751266), (0.17057532881756568, -0.19611325925047723), (-1.6233463196350184, -1.1084095235567295), (-0.5620123562960189, -1.48431184880035), (-0.29358699429273727, -0.4698841976000754), (-0.9201419516259545, -0.9078195413273737), (0.35841248868764697, -0.25835183333572553), (0.8206214999093044, 1.3604839888767948), (-1.1861243639397472, -2.099070335232998), (0.6778252930850656, -1.8620328415764265), (0.8831304098781485, -0.8406255528243772)]


# NOTE - pts gathered from pure boxMuller data
pts4 = [(0.1329547571107651, 0.4174454457924009), (-0.04119582480976863, -1.1455025368189868), (-0.7326098061004434, -0.30280238243218743), (-0.010752984987668829, -0.817266846515145), (1.0926763231998833, -0.4281354772613932), (1.1295999707055826, 1.097427159567858), (-0.08224718907193532, 0.5978784721667417), (-0.08347862813990951, -0.3941699537016038), (1.7607891546101526, -0.2657312967665527), (0.9599632447386836, 1.9855791805716774), (-0.526822954423701, -1.203397271742817), (-0.9323108532113976, -0.32849793851883163), (0.2471149513502864, 0.1916880218051872), (1.4130285606167263, 1.0794859406986879), (-1.4537868622017156, 0.4599800140101471), (-0.9036922651205055, 0.14821202724095037), (-0.14348358608695758, -1.3401645175524384), (-0.1520712034317182, 1.0567645778602073), (-1.0263777526935867, 0.7663651471019817), (0.5491918716952373, -2.445189319725199), (-0.010888806943123405, 0.3699460028848422), (2.140064455297639, 0.47890651846513743), (-0.1384062978674084, 0.1883686906966578), (-0.05964869273445686, -0.07805037163483945), (-0.3547698275111905, 0.019002207189122745), (1.3739775724364567, -0.0507892597390072), (-0.7003533462065719, 0.6243498581272098), (1.3973227161020372, -0.4528708658490487), (0.6258176232409831, -0.10184075375061856), (1.3687478449132238, 1.177592665098917), (-0.5322051296858487, 0.4059222134054123), (0.28058002041285046, -0.8055004520666602), (1.2696295792169345, 0.9824131490571573), (0.02372734350689551, 1.6327423875234368), (0.17930784775210987, 0.36607223817634954), (-0.7018091746274417, 1.3993521250277625), (-0.6348049295170625, 0.07745010547666224), (0.9094562440419743, -0.2707814731350759), (-0.700050342988086, 0.6825414865644098), (-0.1241966195892125, -1.1465320439736375), (0.956561593425486, -0.5218861347946321), (-0.5684846127356438, -0.9990716805144991), (1.380451426811325, 0.27542951079209393), (1.2562719170932317, -0.3331704375571198), (0.7774900493278385, -0.13372551717716402), (-1.5923298099735352, -1.2181729544836948), (-1.1370101197272726, -0.47708752979571534), (0.03983407286938908, 0.3410286991443944), (0.9891715649936033, -0.3551496074191808), (1.4255346608212784, -0.23531335577378368), (-0.2007452009820609, 0.12482291271574679), (-1.1223747669606547, 0.9948142587543147), (-0.12344343677889824, -1.4848609779560185), (-0.28971898418850567, 0.3202177982741398), (-0.2716129034429306, -0.8693146146616915), (0.9341958478057824, -1.4573222230859166), (0.9047038974852879, 0.0742840547331411), (-0.8992207588129569, 0.6947166615853876), (-1.3064047744822302, -1.2135122886958594), (-1.25142840250515, -0.02170423581266115), (-0.723624760099497, -0.014100014978684034), (1.5509924188588913, -0.5167713581629702), (-1.630926832870594, 1.331646670736043), (1.9003788431998974, 0.2695719632935033), (-0.5946885907703775, 0.15677214361950015), (-0.22703467739957123, -0.35177899909215377), (1.8614027794814068, 0.5128507067320957), (1.0543189650012381, 1.914479953988809), (-0.8316118644548613, 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-0.15232448490196876), (0.18063597813201668, 0.2970019729244307), (-0.05159167926622937, 0.8794104312057052), (0.16393069381210085, 1.9150361631493287), (1.4094870832418496, -1.5468962743741923), (0.0816274712401615, 0.6184865859199185), (0.5234949153181601, 0.4323688644127795), (-0.44743725602937756, -0.554735784473421), (-0.778362387959257, -2.0744847448923553), (-1.7485333758573913, -0.41682523525236886), (-1.564107550944116, -0.06197014595099117), (-0.830238896132974, 0.3874878046996942), (1.699194193849926, -0.003500926919381841), (-0.9328794584282041, -1.9321774570372148), (-1.3540513799503295, -0.6062807623752499), (0.4940248832184044, -0.4269079478152652), (-1.4613966590661682, 0.9865025570266759), (-0.4730276676931078, -1.2120278237727407), (0.7515335336428439, 1.167821065908072), (-0.9064223796829961, 0.9038076795769427), (-0.20410351506327784, 0.9712899768351443), (0.4064961953148732, 0.9102324339012529), (-1.6102191370131516, 0.2534748466977328), (0.9443746924142429, 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(-1.7748149366293788, -0.2799912731438436), (0.24300880017839208, -0.16538942856464603), (1.165466271657443, -1.9083568132031106), (0.7682346135264859, 0.08687803010581273), (-0.34314936312547933, -0.594165748946945), (-0.40399511615764383, -1.7075800412856061), (0.75236548516682, -1.5628426358314895), (1.0207540216996212, -1.7530767790571284), (0.568928451243457, -1.8425551287131092), (-1.8196219862085026, -1.181090993116177), (-0.129274375816266, -0.6699540100459456), (-0.3959109410090682, 1.4659168643285307), (0.5613242794598324, -1.7687999601230115), (-0.5425879072780297, 0.0964398486632196), (0.61907488914385, -1.1108702890452988), (0.6165043728912171, 1.714894960102285), (-0.48343012357227877, 2.479877091391564), (-1.1154536339542813, -0.38126405548402675), (-0.1782374167732536, 0.37220023139834724), (1.5151924707740294, -0.021763913508781794), (0.08005955138509105, -0.36497545054042974), (0.5931539785406064, 0.007005919370705847), (-0.699949037047703, 0.8401004967210058), (-0.7931035594119228, -1.1950892161449655), (-1.4454711510177285, -0.3379187696961425), (-0.31408530268900353, 1.6935300770861772), (-0.2921280268227762, -1.0332269033015933), (0.09031544771331092, -0.6726671518900218), (-0.5288290820270939, -0.3935800273837423), (-0.5942281574654185, 0.08484623598275164), (-0.5844248570836578, -1.7978759433508655), (-2.009417815763085, -0.6060495644620071), (-1.1495577097677876, -0.24447572149505317), (-0.39721130365783713, 0.5180469916520942), (0.5178111078622654, -0.3370502967962804), (-0.4636462848984722, 0.5044198055964133), (0.43954877136123804, -0.4806305347293591), (0.6901346879643158, -0.19104624562623213), (1.2247161311096024, -1.2748398259255798), (0.702917062046399, 0.08819400509744921), (0.5496967907613854, 0.23160382526656897), (1.2331974329599407, 0.04677896477941651), (-0.29910202147559467, -0.799912731543223), (0.7954093155169201, -1.4252638277869765), (-0.12585646552112126, -0.8614308775078323), (-1.1479374469032304, 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-3.1890814184761873), (1.5020993080122185, 0.30807443532064743), (0.5621883600792922, 2.3441702404381504), (-1.4339189476683512, -0.3200504520718987), (0.7062371093720826, 0.3154673427969188), (1.8862426983014764, 0.9612609199482661), (0.008351635899535524, 0.32284128145947916), (0.26473651605661663, 0.8712431348756449), (1.400246044941893, 1.3717484096486336), (0.19687921737024128, -1.2689293705068034), (1.4846498693422772, -0.39453068571209987), (-0.22583930197804988, -0.32024925288126566), (-0.8896777487965211, 1.3031207292347404), (-0.5500443705935013, 0.03222869836589995), (0.10991720266591566, 0.0989015159543067), (-0.31059126882478794, -0.2448665092662374), (0.3845848228888991, 2.4279720571431525), (0.7535976766163265, 0.1653454312174672), (-1.627150154201514, 0.2690712266013933), (-0.014605206259134832, -1.6927558480710834), (-1.0400551292795417, -0.983161340315106), (-0.6183420207740923, -1.2186437032774646), (-0.3384742541803026, 1.2537815878070653), (-0.6876705481328892, -0.34848400061095763), (-0.7265147326683572, 0.8636354821749721), (0.2766697538594947, 0.15395319417560693), (0.3331312211197139, -0.1975495585046043), (0.628679747596652, 1.6346038301448917), (-0.16799575495178057, -0.6325097935187997), (-0.3302149752014328, 1.547903843960998), (0.32838107829340707, 0.13359785637861163), (-0.3463310774752681, 1.3586282403435104), (-1.0568013002228698, 0.29014954694364314), (1.501075867725849, 0.22673660386159006), (-0.048784302330145544, -1.6831991786159943), (0.02097536653908595, -0.45114665945243276), (-0.22874768699372347, -0.9579034596990494), (1.1493676529948795, 0.522838369884201), (0.42512181303599883, -0.05184192666761593), (-0.8251447945447135, -1.3332372163345123), (-0.32088148139778744, -0.3374031029900594), (-1.2322883841226953, 1.8097592838987644), (-0.14931374900958647, -0.3526229058532551), (-0.9890104408344242, -0.45856854791148616), (-1.4326097855933995, -1.8211058987984081), (1.3815165969187053, 0.04983267135529731), (-0.34084686613125764, 0.1180918097474005), (-1.8583476869186806, 0.9323852057752339), (0.2286443419286723, -0.008324297822700144), (-0.02875564434494628, -0.8889720500597258), (0.8813629909033913, 0.24086566244924396), (-1.156904910883826, 0.17967226514154294), (-1.5542064784647873, -0.48284492269445956), (1.4927943844774207, -0.08688321891946856), (0.665577422069672, -0.4564730228926854), (0.9630748069107439, -0.45602469118616656), (0.13908777265387168, 1.890397295439342), (0.1529301301079963, -0.4240050037067942), (0.3938521261683922, -0.24873373023255183), (-0.991495386922608, 1.0328858806768022)]

# NOTE - pts gathered from data points after using boxMuller.lat as distance and rotating around randomly
pts5 = [(-0.10029382269509757, 0.023119033266104202), (0.3352873054339509, 0.7981901444654879), (0.08009074409386023, -0.11049501641961107), (0.1907267894209397, -0.3547238435014039), (0.6371881049374836, -0.7182800397918213), (0.5552237240662986, -1.233553372374827), (0.00472388606472159, -0.05177663420531261), (0.030464173220738428, 0.11966616982149436), (-0.36983978312912724, 0.09466630586384413), (-0.42611623342510063, 0.22956209343183118), (-0.5738020883984146, -0.38044650963804266), (0.6796855544903424, -0.7765173208735883), (-0.15807177510417025, -0.06295779871476657), (-1.0008724707622076, -0.17744141687936246), (0.6518529225786108, 0.009645273471470425), (1.2023967250617649, 0.6846286150708428), (-0.19563776556153423, 0.2735702407998523), (0.9717240893043989, 0.7884663935021653), (0.5896075567208594, -0.053106552947614294), (0.0024729049453797954, -0.014473046675800903), (-0.004028366234792045, -0.0038940043434651374), (-0.03304454888716168, -0.055334262504722564), (-0.45392825456809505, -0.2013087869631703), (0.07508184747995945, 1.289657855517943), (-0.0009462955700734786, -0.0010897348131142144), (0.15874836446503363, 0.11977229818128868), (0.5892184592513896, 0.06739602901200767), (-1.2647015430205097, 0.10017394958075475), (-0.20536146589246126, 0.18812991222950007), (0.7508465535789882, 0.07427108479432501), (0.014576811986826695, -0.713841123020783), (-1.2520501881132715, -0.5833149555171427), (-1.3263682915440966, 0.2153820323282509), (-0.4735709902502961, -0.17874766146729004), (-0.6892298400525791, 0.3790569212233105), (0.37657312839753987, 0.06142131958799086), (-2.2215031229265354, -0.19186779944773794), (0.17420999341318022, -0.472343305307588), (0.2749945154929291, -0.029124523379801846), (-1.2429656373935922, 0.27234833055252305), (-0.16234013040729509, 0.34178442841908546), (-0.01707179133072489, 0.27267556660499254), (0.7504670464719934, 0.9670472224304517), (-0.08709610292314972, -1.3465236919352424), (0.4738686081778087, -1.060777931546367), (-0.8503435478006576, 0.04667211548188304), (0.10739018138070926, -0.09836774144983217), (-0.06027146859035232, -0.15378286163960433), (0.47304800249915063, 0.1409936064266924), (-1.424603600948721, 0.5006049973447393), (0.16731358611921113, 0.2158442212265527), (-0.2847123855810976, -0.23360873696567455), (0.1843533401147093, -0.1527481803122043), (0.5019032434407009, -0.24984369194163808), (-0.21322345202452583, 0.2129174375855249), (0.008237301034969658, -1.1698881132524441), (-0.4478272545129348, 0.163222017062501), (0.5238520768260935, -0.18688003024598185), (-0.1260808351867294, 0.04555023994362196), (0.09474910475528854, 0.05475355901202331), (-0.00202380032701996, 0.01461970994590069), (0.16541337266727577, -0.13553346635553887), (-0.48615146443817076, 0.2188684204700621), (-0.727346457995346, 0.897999446329526), (-0.016296636827614036, 0.026758216375499425), (0.03504087659916234, -0.4210387920576824), (-0.02567622068832949, 0.14460316072662607), (0.21799592891780492, 0.17237373180151658), (-1.0684323707391106, 1.0571265122287183), (0.058674224188564265, 0.15664873925221273), (0.21134169200647404, -0.28912233788284963), (0.009718420841001694, -0.5000225638098214), (-0.14595559314127513, -1.0358071129267568), (0.3846545323440682, -0.10588134796230712), (-0.10705547834350398, 0.3476570115611865), (-0.03159861671207698, 1.054712692577961), (-0.001355915774658074, 0.0056669166793232644), (0.12923215762708276, -0.19422046141481256), (0.09746910933846015, 0.3333348897683055), (-0.4273921055127251, 0.1591594818398726), (0.14930647676663844, 0.48009475141701513), (0.5638655643278602, -0.34791481504088323), (0.6491363063032316, 0.6230454192508763), (0.6103350836716324, 0.8172530806200446), (0.018046546754268582, -0.7705868407340921), (-0.6830294445382056, -0.08753142949452376), (-0.8023459447700504, 0.8879573799716483), (-1.0307715121112868, -1.3321378315760397), (0.4308752756339018, 0.06503190584593942), (-0.26536524078505536, 0.293369585904546), (-0.10369687264863564, -0.7087097056065493), (0.4352013448667607, 0.15824944752589148), (0.733481572650423, -0.3073001649413609), (-0.2571900242174755, 0.6359890136276104), (0.026036767516936527, 0.11814457436857304), (0.7158376259964669, -0.12683011222705967), (0.2206006410569995, 0.2248754180273763), (0.5351638447748169, -1.4943639213760787), (0.7695893131053824, -0.253391365386012), (0.8902143962892195, -0.9986193354055434), (-0.054115304902185545, 1.7156015059727958), (1.7339370346513179, -0.4330037650648795), (-0.6962328747443461, 0.3237257965183262), (0.1396575387722853, 0.22840764780194053), (0.6596115722167685, -0.22211644766968222), (2.0548158938779406, 0.713683722789189), (0.10092345992417923, 0.08174162469112617), (0.5445685082677894, -0.9186327203973454), (0.21340808322737218, -0.183487631008131), (-0.6047194341105971, -0.4774410050845027), (-0.39880159777804464, -0.026721485639212745), (-0.2239836645773029, 0.17898540258707876), (0.37073821128778434, -0.9140237928894094), (-0.29805455676244436, -1.1397573668960643), (-0.02739712482041389, -0.0018279713975512836), (0.29781741793517563, -1.3409414186714659), (0.01240602900061978, -0.15041278001836778), (0.06685506411633466, 0.4384836503325141), (-0.17576451139070612, 0.13961811558550197), (-0.6777611122536518, 0.16122951009881034), (-0.15183816039012873, 0.5427228216053913), (0.09400892552734252, 1.2006415254896587), (0.6105114908232576, -0.8429791899133171), (-0.3692839821734948, -0.6251813729546551), (1.3061545195065782, 1.1894083018693378), (0.11698280943832737, -0.4649246296928959), (0.1745586968102102, -0.3570540180422846), (-0.9321817335558221, 0.6321077412464174), (0.03502178850159698, -0.1304038422935463), (-0.19141877053185863, 0.26147245166842004), (-0.0880687185327, 1.2536423207984189), (-0.331935810475526, -0.4774373953380184), (0.3321925235932113, -0.16702308855425074), (-0.8755811867188651, 1.5321229659076931), (0.22559547064619828, -0.3312908005102581), (0.10740821711959295, -0.3171059157729139), (-0.003573410433093886, -0.025426897141290174), (-0.47026523105668294, -0.07725905029369617), (-0.3699033387875513, -0.10585637716487224), (0.046726386126356205, 0.15614609597074974), (0.0034334805439601786, -0.010168366577439688), (-0.6649488600719938, 0.2459593430771915), (0.47369779925249295, 0.24098924062652732), (0.8192115803266233, -0.9988446717918359), (-0.755083564313222, -0.49542005455318666), (-0.09453784497986087, 0.9673778664280005), (-0.5509133247691831, 1.2768791654737435), (-0.07917321716634987, -0.3877139487194609), (0.12335229378304174, 0.2558016403842619), (-0.8117700668745673, 0.7253386579791186), (-0.9215152936045796, -0.7545447778646449), (0.9179376712274528, 0.16652369541258025), (0.02858970066034408, -0.14495069439330452), (0.09660934820505436, -0.029652634093504687), (0.4702046255001864, 0.326835609879863), (0.014590058517484294, -0.6844908227630704), (0.4039343356422628, -0.5804198183128771), (-0.07488396843297589, 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(-0.6126671502256514, -0.7277911241501017), (-0.1332866222946749, -0.8879695414381501), (-0.23608127738158952, -0.3584533564068079), (0.5370499927070181, 1.025579438070592), (-1.333620151678821, -0.6458685734911225), (0.26776643174637965, -0.9101925423530904), (0.4979132508975604, 0.03896558788583716), (0.2766863284542577, -0.009476318897468068), (-0.40008252243466924, -0.833596890931975), (0.1540085010394898, -0.2624950197808778), (0.5232026491178238, -0.1485161684406386), (0.4175632360337816, -0.8218454063487878), (0.1334629764162073, 1.1879484374217646), (-0.04128883153514759, 0.36745738237961556), (-0.37798449618347824, -0.06941364764190926), (-0.0887719554628964, -0.08761097053359172), (-0.695795696972505, -0.5086556315779115), (-0.4257556084775921, 0.12696275890737638), (-0.18831108725772455, -0.04819386067158257), (0.385046708526825, 0.3533642003233001), (0.4524259221189007, 0.08090830165278937), (0.5564609079450666, -0.5320309381560251), (0.8801791653824135, 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0.1654605650515456), (0.2541865051299623, 0.17403137781425806), (0.329276210242854, 1.1298840872296039), (-1.5183618652667907, -0.7828205063709829), (-0.030011743771613274, -1.3568771271720579), (-0.07805070483044717, -0.27493689719358366), (-0.256292741693197, -0.5830941236850679), (-0.43895160825744794, 0.7029389329580701), (-0.015585588734568511, 0.0008515892287553849), (0.6461535318562505, -0.6246768349822006), (0.6993353968843874, -1.1386317578477523), (0.9196321967259097, -0.046002711575623356), (1.0519108503536645, 0.9853284024188558), (-0.06914102823427856, 1.5377917505164802), (-0.4339951055148017, -0.05453949011504936), (-0.08240834603808012, -0.25047911586597305), (-0.3276661506476865, -0.2916849157104801), (-0.0912281125803855, 0.36288519779668876), (-0.0037974099078004653, 0.26485086363461563), (0.6818230216713712, -0.385019964879498), (-0.7624371515730244, 0.6327258138745678), (-1.470095054743873, -0.17554375770386146), (-0.03463988936970695, -0.04980887881444013), (0.1412068485914956, -0.03183768959153841), (-0.012354510731098271, -0.022557463993959474), (0.053208555500765205, -0.7779563821744543), (0.2821139667140347, -1.7738245199943157), (-0.6658274933673892, 0.6074047630784918), (-0.07705003707287905, -0.5596314320379147), (0.15701698195836736, -0.44461222056889027), (-0.6579431485582494, -0.5214587411299375), (0.007366037115075096, 0.06894730620814253), (-0.5289625901254048, -0.06380037876692723), (-0.10101575480592892, -0.000848190008635231), (0.08925012071134163, 1.1497761177929995), (-0.0999646649688098, 0.41048040598962726), (-0.326653933527645, 0.40249875473875063), (-0.022074388239026015, 0.024328303340038812), (-0.004596805507062414, 0.09828412546390368), (1.5472106340192753, 0.35997468776640423), (-0.4741366510139104, -0.4678628422451537), (0.5623675312795787, 1.1046027468653437), (-0.6255491293728737, 0.549766924290158), (0.30210485156002304, -0.04844014530587997), (0.21091722304267257, 0.5808511602101223), (0.05881864641295737, 0.002508278132681751), (0.4098445256359339, 0.28029862125418703), (0.05304014171122144, -0.4101838411676423), (-0.9199674884353947, 0.6302601424194362), (-0.2410127601931138, 2.4116847291715455), (-0.2721159607129055, -0.22826115436704789), (-0.23273088549027024, -0.22511909896391785), (0.25852835311452504, 0.6751643132189723), (0.24741866339005927, -0.6252788537017233), (0.06385515389151225, 0.042439076371772945), (-0.2394007651545174, 0.060891607534313545), (0.27481287963226225, -0.2622060256090107), (0.5867079856684518, 0.464688780290405), (0.31844590576408843, 0.4571978636401693), (-0.12588634414758879, -0.03608101026860023), (-0.26206169300373633, -0.21261752188826025), (-0.4488790353793223, -0.6139018298842113), (1.3436282737953866, -0.4243076041923482), (1.1444992952005033, 0.2086261889441494), (-0.7206362250866132, 0.46748135182431577), (0.08116066195017531, -0.22350658654704522), (0.7981872604965998, 0.9666819848404664), (0.6035625900502842, 0.9671089427404029), (0.3972050835255227, 0.4080530410632081), (0.23402222708166592, -1.0497550910471325), (-0.07262711284598786, -0.5302443815401494), (0.10128856687018321, -0.009569394844487746), (0.07462914224868299, 0.07103016361706947), (-0.39820859864891006, -0.12629091182221788), (0.8536231987214452, 0.8339100533663941), (0.1638646229287726, 0.4735151662218006), (1.2321048624864448, 0.27620280780269535), (-0.1290548166893596, -0.2530278300659582), (0.38323809084578, 0.3660009404948461), (0.1208585824261782, 0.4059814615175101), (0.25139452205618396, -0.41949694827597606), (-1.1267831890484752, -0.08957318934442632), (0.22860312875637392, -0.02858512402319332), (-0.4806640282653319, 0.37837301336481655), (0.7942928354781045, -0.4811427433991939), (-0.29561607524164574, 0.37292631943124677), (-0.12012206104408253, 0.082635164514611), (-0.301146828623824, -1.1862862080441754), (-0.06097379137219418, -0.026812588205705045), (-0.6053308873894967, 0.7303494973564418), (-0.19201737137857464, 0.34878993698270455), (-0.0859339457521925, 0.3818864955382026), (0.5744764217107057, 0.12050967116069794), (1.100790693828097, -0.024650292615430242), (0.2645284247501968, -1.0998543796714093), (0.17612616410234055, 0.21186123226389703), (-0.9018655437583647, 0.4894052917305879), (0.5435764061757856, 0.2142629113062528), (0.3222666040704663, -0.49308637182467757), (0.40935804778981905, -0.8459389018109913)]

vals =[0,0,0,0]
for p in pts:
	val = haversine( (0,0),p)
	if val < 100:
		vals[0] = vals[0] + 1
	elif val < 200:
		vals[1] = vals[1] + 1
	elif val < 300:
		vals[2] = vals[2] + 1
	else:
		vals[3] = vals[3] + 1
		print str( val )
		
	#print str( haversine( (0,0),p) )+" - "+str(p)

print "<1sd: "+str( vals[0] )+"  1sd<=x<2sd: "+str( vals[1] )+"  2sd<=x<3sd: "+str( vals[2] )+"  >3sd: "+str( vals[3] )

dms2dd((84,33,14))
dms2dd(EL[0])    # The zero-th element in EL is the lat.
val1 = dms2dd((84,33,14))
val2 = dms2dd((81,21,12))
#print val1 - val2

ELdd = (dms2dd(EL[0]), dms2dd(EL[1]))
SSMdd = (dms2dd(SSM[0]), dms2dd(SSM[1]))

# The next two lines should be the same:
EL
(dd2dms(dms2dd(EL[0])), dd2dms(dms2dd(EL[1])))
#print str( haversine(pts[0], pts[1]) )

elssmDist = haversine(ELdd, SSMdd)
#print 'the distance from East Lansing to the Soo is ' + str(elssmDist) + ' km.'

